# 307

This number is a prime.

The square of 307 is palindromic.

El Salvador has 307 kilometers of coastline.

307 has period length 1^{3} + 5^{3} + 3^{3}.

The Area Code for Wyoming is 307.

The smallest number that is the sum of any set of primes containing all digits: 2 + 5 + 41 + 67 + 83 + 109 = 307. [Gallardo]

In the movie *The Odd Couple*, when Felix checks into a hotel, the first room the desk clerk tries to assign him is 307. [Litman]

The largest number that you can type in Excel
is 9.999 * 10^{307}. If you type in a larger number,
Excel will treat it as a character string. [Andrew]

*The Grass Roots* set a record for being on the Billboard charts 307 straight weeks. This was bound to happen "sooner or later."

Curious Book Shop is a used and rare book store located in downtown East Lansing, Michigan (307 East Grand River Avenue).

Smallest of the first case of seven consecutive primes that remain prime if you eliminate their first digit. [Loungrides]

Smallest nonpalindromic prime with a palindromic square. The next one is 30001253. [Gaydos]

The smallest prime whose reversal is a Kaprekar number. [Loungrides]

307 permutations of the digits of 2^20 (1048576) are prime numbers. [Gaydos]

Dmitry Kamenetski found that if f(0)=307, then f(n)=3*f(n-1)-574 generates thirteen distinct primes in a row. [Rivera]

307 is the smallest prime for which 2 and 3 are cubic residues. That is, the congruences x^3=2 and x^3=3 mod 307 both have three solutions. [Drost]

307 and its prime index (63) are both reverse triangular numbers. Are there any more examples of this property? [Gaydos]

Arnault once found a composite number for which all bases less than 307 are strong liars.